已知函数f(x)对任意的实数a,b都有f(ab)=f(a)+f(b)成立.
1)求f(1)与f(0)的值
(2)若f(2)=p,f(3)=q(p,q均为常数),求f(36的值.
人气:381 ℃ 时间:2019-08-20 21:18:46
解答
(1)
令a=b=1
f(1×1)=f(1)+f(1)
f(1)=f(1)+f(1)
所以f(1)=0
令a=b=0
f(0×0)=f(0)+f(0)
f(0)=f(0)+f(0)
所以f(0)=0
(2)
f(36)
=f(2×18)
=f(2)+f(18)
=p+f(2×9)
=p+f(2)+f(9)
=p+p+f(3×3)
=p+p+f(3)+f(3)
=p+p+q+q
=2(p+q)
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